SEGURIDAD ESTRUCTURAL DB-SE

non-convex shape and can therefore not accurately be described by a convex hull-based method. Furthermore one may notice the large loss of information by only making use of the result of the convex hull-based method. Opportunities, with respect to engine calibration efficiency and finding the true optimal point, lie in the field of describing high dimensional non-convex shapes.

Figure 2.8.: The found local convex shape converted to the global engine map [29]

2.2. State of the art methods for design space description

and determination

In this section an overview is presented of other implementations and studies of design space description or (online) determination methods. In Section 2.2.1 the currently known software tools that are used for engine calibration are described. The section focuses if and how constraints on the design space are implemented. Section 2.2.2 gives the known publications on the topic of design space description and determination.

2.2.1. Software applications

The known software applications are explained below. Some applications are in-house developed tools by car manufacturers themselves. Other tools are developed by research companies that explicitly focus on the development of software and methods to support engineering tasks. The tools are listed alphabetically by the name of the application.

ASCMO by ETAS GmbH

ASCMO is a tool developed by the company ETAS GmbH and can model and optimise relations between in- and output variables of an unknown systems, making use of DoE. It can imple- ment constraints on the measurement range of one of the input variables, depending on one or two other input variables. These constraints can be selected ‘visually’ in the graphical user in- terface or by means of loading known or engine project related characteristic maps or curves. [12]

CAMEO by AVL List GmbH

CAMEO from the company AVL List GmbH is a tool designed to run ‘intelligent engine calibration procedures’ (iProcedures) in a testing environment [3]. It has been created in cooperation with automotive manufacturers for combining DoE methods with automated test sequences. The DoE package of the tool can implement constraints from engine maps and curves and line constraints in the design space, though the number of variables is for the design space calculation is limited by eight. According to [3], the design space is a multi-dimensional convex hull calculated by means of all measured variation points that did not encounter any limit violations. Furthermore the online range detection in the package ‘CAMEO ONLINE PACKAGE FOR TESTBED USE’ can also determine the design space online during engine operation. The result of the range detection can also be implemented in the ‘ONLINE ADAPTIVE DOE’ package [2].

EasyDoE by IAV GmbH

EasyDoE is tool developed by the company IAV GmbH also to implement the DoE methodology [15]. It builds data-driven simulation models which can be used for the optimisation of engine maps. The tool allows for the integration of complex constraints, such as multidimensional convex hulls. The so-called Boundary Finder can determine the engine constraints online and also makes use of a convex-hull based method. According to the company the BF can cope with large design spaces and with non-convex design spaces, as proposed in [22].

mbminimize by the University of Tübingen and the BMW Group

The mbminimize algorithm was developed by a cooperation of the University of Tübingen and the BMW Group for meeting the increasing demands of the calibration of modern combustion engines. The tool contains an automatic online optimisation algorithm for complex nonlinear sys- tems with nontrivial search space dimension [24, 34, 49]. The design space is implemented in the so-called tool ‘limit handling’. The algorithm implemented limit models using regression models, classification models, and geometric models. A special technique based on confidence terms is implemented for controlling restrictiveness of the models with arbitrary precision [23, 24, 49].

Model-Based Calibration by The Mathworks

The Model-Based Calibration toolbox by The Mathworks is a design tool developed especially for calibrating complex powertrain systems also making use of statistical modeling and numerical optimisation. The tool can also implement constraints on the set of input variables [45, 46]. Ac- cording to [46] the boundaries implemented can be an ellipsoid, a hyperplane or linear constraint, a 1D lookup table, or a 2D lookup table. The documentation in [45] explicitly states that the tool can implement boundaries making use of a convex hull that contains the minimal convex set of the data points, an ellipsoid describing the minimum volume ellipsoid for all data points, a star-shaped interpolation of all data points on boundary and a normal data range for each input.

2.2. State of the art methods for design space description and determination

Rapid Hull Determination by Daimler AG

the Rapid Hull Determination (in German ‘Grensraumvermessung’) is a Daimler internally deve- loped algorithm by Peter Renninger [36]. The tool uses a convex hull-based algorithm and is designed for an online determination of the design space. Starting in a pre-defined safe starting point, stepwise increments along the variable axes are taken and measured until the boundaries have been reached. For more details see also Section 3.1.2.

2.2.2. Publications

Below the remaining known publications on the problem of design space description and determi- nation are listed, that do not belong to any of the tools described in Section 2.2.1. The first three publications make use of a convex hull-based method and propose an extension to the Rapid Hull Determination method proposed by Renninger. The last section shows the publications that are proposing to use support vector machines for describing the design space boundary.

Adjusted Rapid Hull Determination - Transformation to spherical coordinates

A collaborated research project was started at the ‘Research Association for Combustion Engines e.V.’ (Forschungsvereinigung Verbrennungskraftmaschinen e. V.) in 2010, having both industrial and academic partners discuss the challenges and possible solutions on the topic optimised fast online measurements covering static and dynamic engine models [25]. The project report also proposes an online implementation of the design space, extending the Rapid Hull Determination of [36]. For non-convex boundaries a polar Delaunay-triangulation with a known inner central point can be calculated. A transformation of the points from the normal Cartesian coordinates to spherical coordinates is for the calculation required.

Adjusted convex hull Rapid Hull Determination - Changing the start points

Also the method described by [22] is extends the Rapid Hull Determination of [36]. The first iteration of the method is the same, but the starting points for the next iterations are the known safe points and not the centers of gravity of the calculated hyperplanes. A safe starting point is defined as the nearest point to the intersection between the previous ‘setting vectors’ and the calculated normal vector that is crossing the center of gravity of the hyperplanes. The last step allows for non-convex boundaries as well.

Adjusted Rapid Hull Determination - Continuous limit approach

The continuous limit approach, as proposed by [30, 39], determines the design space making use of a so-called ‘slow dynamic slope method’, where the variables are, instead of discrete steps that are separately measured, continuously adjusted. The measurements required to find the boundary do take place under stationary conditions. The results is described by means of a convex hull. According to the author [39], using a convex hull-based method enables a fast modelling and analysis of the described hull.

Support vector machines

Using support vector machines as a design space determination tool has been introduced by [5]. Nevertheless the thesis does not provide a solid solution to the parameter selection. It suggests to use heuristics related to the field of application. The paper presents an online design space determination. It uses part of a known data set to train the SVM, adding new points to improve the result. A different part of the data set is used to validate the results to define a stopping criteria.

The presented thesis continues on the topic topic of SVMs as proposed by [18, 19]. Intermediate results on the use of SVMs related to the other proposed methods of convex hull-based and confidence intervals, as well as a method for determining optimised values for the SVM parameters have been presented in [20].